Then \({S} =\nu _\beta \cup \lbrace  h_\sigma \rbrace \)  is the generating set for \(\operatorname{FMap} (T)\)  given in
[1]}. We now equip \(\operatorname{FMap} (T)\)  with the word length associated to this
generating set which we denote by \({{\mathchoice{\hspace{0.55542pt}\mbox{$\centerdot $}}{\hspace{0.0pt}}{1}{m}u}{\hspace{0.55542pt}\mbox{$\centerdot $}}\hspace{0.55542pt}}{\hspace{0.83328pt}\centerdot \hspace{0.83328pt}}{\hspace{0.83328pt}\centerdot \hspace{0.83328pt}}\)\(\operatorname{FMap}\)\(.\)
